The easiest way to solve this equation is by graphing.
To solve a system of equations, you can use 2 methods. You can, one, graph the equations and find the intersection, or two, eliminate a variable.
1. Graphing: we can put the two equations in standard form, or y=mx+b, with m being the slope and b being the y-intercept. So, your two equations are y=x-3 and y=-x+5.
We can see the intersection is (4,1), so x=4 and y=1.
2. Elimination: We can try to eliminated one of the variables, solve for the other, and plug that back in to solve for the other. In this case, let's try to eliminate x.
By subtracting these equations from each other, since x-x=0, -y-y=-2y, and 3-5=-2, our new equation becomes 0-2y=-2. If we divide both sides by -2, we get y=1. We can then take any of the original equations, x-y=3, and plug it in. So, x-(1)=3, so x=4.
May 21st, 2015
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